Related papers: Non-monotonicity of trace distance under tensor pr…

Given a positive integer k, it is natural to ask for a formula for the distance between a given density matrix (i.e., mixed quantum state) and the set of density matrices of rank at most k. This problem has already been solved when…

By carrying out appropriate continuous quantum measurements with a family of projection operators, a unitary channel can be approximated in an arbitrary precision in the trace norm sense. In particular, the quantum Zeno effect is described…

In order to construct a measure of entanglement on the basis of a ``distance'' between two states, it is one of desirable properties that the ``distance'' is nonincreasing under every completely positive trace preserving map. Contrary to a…

Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, and theses definition usually fail at…

Mixtures of coherent states are commonly regarded as classical. Here we show that there is a quantum advantage in discriminating between coherent states in a mixture, implying the presence of quantum properties in the mixture, which are…

In the present paper, the trace distance is exposed within the quantum operations formalism. The definition of the trace distance in terms of a maximum over all quantum operations is given. It is shown that for any pair of different states,…

A generic model of measurement device which is able to directly measure commonly used quantum-state characteristics such as fidelity, overlap, purity and Hilbert-Schmidt distance for two general uncorrelated mixed states is proposed. In…

We investigate the exact dynamics of trace distance discord by considering two qubits under dephasing whose states belong to a class of $X$ states beyond Bell diagonal form. The necessary condition for the occurrence of freezing trace…

Quantum discord is a manifestation of quantum correlations due to non-commutativity rather than entanglement. Two measures of quantum discord by the amount of non-commutativity via the trace norm and the Hilbert-Schmidt norm respectively…

We propose and present a concept of Topological Distance (TD), obtained from the integration of trace distance over the generalized Brillouin zone, in order to characterize the topological transitions of non-Hermitian systems. Specifically,…

We propose a non-Gaussianity measure of a multimode quantum state based on the negentropy of quadrature distributions. Our measure satisfies desirable properties as a non-Gaussianity measure, i.e., faithfulness, invariance under Gaussian…

Tensor decompositions have become a central tool in data science, with applications in areas such as data analysis, signal processing, and machine learning. A key property of many tensor decompositions, such as the canonical polyadic…

In quantum information theory, communication capacities are mostly given in terms of entropic formulas. Continuity of such entropic quantities are significant, as they ensure uniformity of measures against perturbations of quantum states.…

We investigate the properties of three entanglement measures that quantify the statistical distinguishability of a given state with the closest disentangled state that has the same reductions as the primary state. In particular, we…

A nice and interesting property of any pure tensor-product state is that each such state has distillable entangled states at an arbitrarily small distance $\epsilon$ in its neighborhood. We say that such nearby states are…

We give a necessary and sufficient condition for a mixed quantum mechanical state to be separable. The criterion is formulated as a boundedness condition in terms of the greatest cross norm on the tensor product of trace class operators.

Continuous-variable quantum systems are central to quantum technologies, with Gaussian states playing a key role due to their broad applicability and simple description via first and second moments. Distinguishing Gaussian states requires…

Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…

The notion of partial trace of a density operator is essential for the understanding of the entanglement and separability properties of quantum states. In this paper we investigate these notions putting an emphasis on the geometrical…

The notion of distance in Hilbert space is relevant in many scenarios. In particular, distances between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon…